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IPMAT Indore 2022 - QA (MCQ) Q33 Explanation
December 28, 2024
Explanation:
(a)
If f(x2 + f(y)) = xf(x) + y for all non-negative integers x and y, then the value of [f(0)]^2+f (0) equals________.
Sol. Given f(x^2 + f(y)) = xf(x) + y
Put x = 1 and y = 0 we get,
f(1 + f(0)) = 1 × f(1) + 0
⇒ f(1 + f(0)) = f(1)
It means 1+f(0) = 1 or f(0) = 0
Therefore, [f(0)]2+f (0) = 0.